The algebraic size of the family of injective operators

Description

In this paper, a criterion for the existence of large linear algebras consisting, except for zero, of one-to-one operators on an infinite dimensional Banach space is provided. As a consequence, it is shown that every separable infinite dimensional Banach space supports a commutative infinitely generated free linear algebra of operators all of whose nonzero members are one-to-one. In certain cases, the assertion holds for nonseparable Banach spaces.

Abstract

Plan Andaluz de Investigación (Junta de Andalucía)

Abstract

Ministerio de Economía y Competitividad

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